using the boost generators \(K_i\)  of the \(L^{\uparrow }_{+}\)  group (having the non-vanishing components \(\left<K_i \right>^{j}_{0} =\left<K_i \right>_{j}^{0}=i\delta _{ij}\)  [1]}). Note that these boost matrices satisfy \(B({\bf x})^{-1}=B(-{\bf x})\)  and \(B({\bf x}=0)=I\) . In addition, we can verify that
\(\Lambda _{[0]}({\bf x})[\Lambda _{[0]}({\bf x})=I~ ~\Longleftrightarrow ~~ B({\bf x})TB({\bf x})=T\,,\) 
